In this prior-art shaving apparatus the drive member is formed by a ball having two diametrically opposed projections. A bore extends through the ball and the projections and is engaged by a drive pin having both ends connected to the cutter, so that the axis of the drive pin constitutes the axis about which the cutter is pivotable on the drive member, which axis extends perpendicularly to the driving end of the swing lever. Moreover, the ball is mounted in a bore formed in the driving end of a swing lever which is pivotable about an axis, its projections projecting from the driving end of the swing lever through slots adjoining the bore. The swing lever is offset relative to the plane in which it pivots to permit a laterally offset arrangement of a shaving-head frame carrying the shear foil, which is frequently desirable in order to make the dry-shaver easier to handle during shaving. As a result, the axes about which the swing lever and the cutter are pivotable on the drive member subtend an acute angle, which means that as it reciprocates the cutter tends to describe a path resembling a conical surface and thus inherently does not perform a rectilinear movement. However, since the drive member for the cutter is constructed as a ball, it can move relative to the driving end of the swing lever in accordance with all on the three possible degrees of movement, thereby allowing the drive member and the cutter connected to this member to be pivoted or tilted to all sides, so that as it cooperates with the shear foil the cutter is nevertheless guided rectilinearly by said foil. Thus a correct cooperation of the cutter with the shear foil is also guaranteed when the shear foil is subjected to a shaving pressure. Because of the three degrees of movement such an arrangement of the drive member at the driving end of the swing lever allows an omnilateral adaptation of the cutter to the shear foil; however, it is found that this does not yield a really satisfactory shaving performance of the dry-shaver under all circumstances. In particular, the shear foil is subjected to shaving pressure in a lateral direction transverse to the direction in which the cutter is reciprocated, which may lead to the cutter being canted inside the shear foil which defines its path. Moreover, since the cutter in principle tends to describe a path resembling a conical surface but is constrained to follow a rectilinear path by the shear foil, additional friction losses will arise between the shear foil and the cutter. This also gives rise to vibrations of the shear foil, inter alia resulting in more noise being produced.